Boundary effects on wave trains in the Exner model of sedimentat transport

Abstract: The aim of this work is to study the effect of imposing different types of boundary conditions in the Exner model describing shallow water equations with sedimentation, when a train of waves is imposed at one of the boundaries. The numerical solver is a second order finite-volume scheme, with semi-implicit time discretization based on Implicit-Explicit (IMEX) schemes, which guarantee better stability properties than explicit ones. We show the effect of spurious reflected waves at the right edge of the computational domain, propose two remedies, and show how such spurious effects can be reduced by suitable non-reflecting boundary conditions.